# What are the use cases related to cluster analysis of different distance metrics?

I'm trying to use different distance metrics like Euclidean, Manhattan, cosine, chebyshev among other distance metrics in my k-means algorithm to calculate distances between the data points and the centers. In what situation would one distance metric be more useful over the other in a clustering scenario? [Comparing all the above mentioned distance metrics]

K-means does not use Euclidean distance. That is a common misconception. K-means assigns points so that the variance contribution is minimized. I.e. $(x_i - \mu_i)^2$ for all dimensions $i$. But if you sum up all these contributions, you get squared Euclidean distance, and since $\sqrt{}$ is monotone, you can just as well assign to the closest neighbor by Euclidean distance (not computing the square roots is faster, though).